Method of identifying properties of molecules under open boundary conditions

ABSTRACT

A method of determining a property of a liquid system, the liquid system including at least one molecule in a solvent, comprises: generating a quantum model of the liquid system, the quantum model including a device region and a lead region, the device region being spherical, paraboloid, cubic or arbitrary in shape and encompassing the at least one molecule and a portion of the solvent of the liquid system, the lead region encompassing a region of the solvent surrounding the device region, determining a first property of the device region by solving a first quantum equation for the device region, determining the first property of the lead region by solving the first quantum equation under open boundary conditions for the lead region, and combining the first property of the device region with the first property of the lead region to arrive at a total first property for the liquid system.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation application of U.S. patentapplication Ser. No. 16/624,833, filed on Dec. 19, 2019, the disclosureof which is herein incorporated by reference in its entirety. U.S.patent application Ser. No. 16/624,833 is a 35 U.S.C. § 371 NationalStage Application of PCT/US2018/040348, filed on Jun. 29, 2018, thedisclosure of which is herein incorporated by reference in its entirety.PCT/US2018/040348 claims the benefit of priority of U.S. provisionalapplication Ser. No. 62/526,470, filed on Jun. 29, 2017, the disclosureof which is herein incorporated by reference in its entirety.

TECHNICAL FIELD

The present invention is related to the field of molecular modeling,and, more particularly, to the use of molecular models to identifyquantum properties of molecules in liquid systems.

BACKGROUND

An accurate simulation of the properties and/or behavior of a liquidsystem, such as a molecule or molecules in a solvent, needs to accountfor the effects of the bulk medium, or “solvent”, which provides theenvironment for the molecule of interest. The solvent is typically anaqueous liquid (e.g., water) although it may comprise hydrophobicmembranes, other organic or inorganic molecules, emulsions, solids,alloys or mixtures of the above. Important solvent properties includeelectrostatic screening, cavitation effects, pH, local interactions withother molecules, viscosity, and the provision of a constant-temperatureenvironment. Some or all the solvent's properties may vary spatially.Temporal changes in solvent properties, such as temperature changes, mayalso occur.

Liquid systems are inherently open quantum systems. In previously knownquantum models of open systems, the system is considered as a deviceconnected between two contacts, namely source and drain contacts. Theopen boundary condition of the system was taken into account by contactself-energies, which represent the charge injection and extractioneffect of the contacts. After the contact self-energies are solved, theelectronic transport of the system is solved by either non-equilibriumGreen's function (NEGF) methods or quantum transmitting boundary method(QTBM) algorithms.

While such previously known methods are effective, the source and draincontacts, which define how the system interacts with the surroundingenvironment, are finite or semi-finite constructs. In contrast, thecontacts/leads of an open system under open boundary conditions aretheoretically infinite and extend in all directions. Consequently, thesource and drain contacts used in previously known modeling methods donot fully represent an open system under open boundary conditions.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a schematic diagram of an embodiment of a liquid systemthat is modeled using the modeling system and methods of the presentdisclosure.

FIG. 2 depicts an embodiment of a model that may be used to model theliquid system of FIG. 1 under open quantum liquid boundary conditions.

FIG. 3 depicts another embodiment of a model that may be used to modelthe liquid system of FIG. 1 under open quantum liquid boundaryconditions.

FIG. 4 depicts yet another embodiment of a model that may be used tomodel the liquid system of FIG. 1 under open quantum liquid boundaryconditions.

FIG. 5 depicts a block diagram of a nanoelectronic modeling system forgenerating

DETAILED DESCRIPTION

For the purposes of promoting an understanding of the principles of thedisclosure, reference will now be made to the embodiments illustrated inthe drawings and described in the following written specification. It isunderstood that no limitation to the scope of the disclosure is therebyintended. It is further understood that the present disclosure includesany alterations and modifications to the illustrated embodiments andincludes further applications of the principles of the disclosure aswould normally occur to a person of ordinary skill in the art to whichthis disclosure pertains.

The present disclosure is directed to methods and systems for modeling aliquid (e.g., molecule/solvent) system that enables the quantummechanical behavior of the system to be analyzed under open boundaryconditions. The model enables open system quantum properties to becalculated for the liquid system. Any kind of observable property may beidentified for the liquid system using the model, including density,solubility, reactivity, stability, optical spectra, thermal spectra,magnetic properties, susceptibility, and the like. The model accordingto the present disclosure is capable of handling any-dimensional openquantum boundary conditions accurately. There is no way currently knownto solve open quantum boundaries in three dimensions. All existingmethods have only finite-area quantum leads.

A schematic diagram 10 of a liquid system comprising a molecule 12 in asolvent 14 is depicted in FIG. 1 . As used herein, the singular term“molecule” will be used to encompass whatever atomic structure that isto be modeled in the solvent, which can be one or more atoms, one ormore molecules, atomic chain(s), solute, and the like. The moleculedepicted in the schematic diagram of FIG. 1 is a benzene (C6H6) and thesolvent is water. In alternative embodiments, similar models may begenerated for substantially any type of molecule in substantially anytype of solvent.

In accordance with the present disclosure, a quantum model of a liquidsystem, such as the system depicted in FIG. 1 , is generated using asuitable simulation/modeling system. An example of such a system isNEMO5. FIG. 2 depicts one embodiment of a quantum model which may beused to model the system of FIG. 1 . The liquid system is considered anopen system. To model as an open system, the device region is consideredas a three-dimensionally shaped region that encompasses the molecule ofthe liquid system and a portion of the solvent immediately surroundingthe molecule.

The model also includes a lead region. As noted above, the lead regionwas modeled as two contacts, i.e., source and drain contacts, connectedto a device in previously known methods which are finite or semi-finitein area and therefore not truly representative of a system under openboundary conditions.

As an alternative to modeling the systems interaction with thesurrounding environment using finite or semi-finite leads (e.g., sourceand drain contacts), the lead region is considered asthree-dimensionally shaped region that completely surrounds the deviceregion and has a shape that matches the outer shape of the deviceregion. This configuration for the lead region enables the leads for thedevice to be handled as being infinite and extending in all directionsfrom the device which is a more accurate representation of the openboundary conditions of an open system, such as a liquid system.

Modeling the liquid system begins with the selection of a base shape forthe model which will define the shape of the device region as well assurrounding lead region. Any suitable three-dimensional shape may beused as the base shape for the model. In the embodiment of FIG. 2 , thebase shape of the model is spherical shape. In alternative embodiments,other shapes may be used, such as cuboid shapes, ovoid shapes,paraboloid shapes, and polyhedrons as well as irregular shapes.Preferably, the base shape of the model is selected to generally followthe shape of the molecule of the liquid system. For example, moleculeshaving an elongated shape can be encompassed by a more elongatedthree-dimensional as the base shape for the model, such as an ovoid,paraboloid, cylinder, etc.

Dividing the system into a device region and a surrounding lead region,the device region and the lead region can be treated separately insolving quantum equations and determining parameters. The parametervalues which are calculated separately for the device region 18 (e.g.,P_(d)) and the lead region (P_(l)) can then be added to arrive at atotal value for the parameter (P_(total)) for the system (See, e.g.,equation (1)).

P _(d) +P _(l) =P _(total)  (1)

Partitioning the system into a device region and a lead region enablesthe system to be analyzed quantum mechanically. One method of analyzingthe liquid system model of FIG. 1 is the Non-Equilibrium Green'sFunction (NEGF) method. The NEGF is the standard approach to modelnanoscale open boundary devices, where coherent quantum effects as wellas incoherent scattering are present. The NEGF method can be applied tothe device region and the lead region separately and then combined toderive properties for the whole system.

The NEGF method requires the solution of the retarded Green's function(G^(R)) and lesser Green's function (G^(<)) in the device to obtain thetransmission and the charge density. The key operation of the NEGFmethod is the inversion of a matrix with the same rank as the deviceHamiltonian. However, the solution time and the peak memory usageincreases dramatically as the device dimension increases. This isparticularly true for spherical leads. For spherical leads, there is apolynomial order 6 relationship between the size, e.g., radius, of thelead and the computation requirements, e.g., inversions, required toanalyze the lead quantum mechanically. The computational load (e.g.,time and memory) can quickly become intractable with larger radii.

To reduce the computational load of the NEGF method, the recursiveGreen's function (RGF) may be used. The RGF method is well-known forimproving the efficiency of NEGF calculations. It allows solving thetransmission and the charge density with only a minimum number of blocksof the G^(R) matrix. The RGF algorithm divides the device intopartitions and solves the relevant G^(R) blocks recursively startingwith a first partition and continuing in forward direction until a lastpartition is reached. Afterwards the G^(<) matrix is solved to obtainthe charge density.

To enable the RGF algorithm to be applied in the present case, the leadregion 20 is further divided into a plurality of partitions (or shells)22, 24, 26, 28, 30. In the embodiment of FIG. 2 having a spherical baseshape, the partitions 22, 24, 26, 28, 30 are each spherical shells 22,24, 26, 28, 30 which are nested inside each other starting at thedevice/lead interface 16. FIGS. 3 and 4 show the partitioning of thelead region 20 in models having other base shapes. For example, FIG. 3shows partitioning of the lead region 20 for a model having a deviceregion 18 that is cuboid shaped, and FIG. 4 shows partitioning of thelead region 20 for a model having a device region that is paraboloidshapes.

The surface area and volume of the shells increase with distance fromthe device region 18. This means that the shell regions which arefarther away from the device have more atoms to consider in calculationsthan the shell regions which are closer to the device.

However, as can be seen in FIG. 2 , dephasing increases as the distancefrom the device region increases (as indicated by arrows 36, 34). Alarger dephasing means that the considered physics is more local in realspace. This also means that the amount of non-locality decreases withdistance from the device region. Because the lead regions farther awayfrom the device region have less non-locality, the amount of time andmemory required to perform the calculations in these regions is less inrelation to lead regions which are closer to the device region.

Once the value of a particular parameter has been calculated for each ofthe shell regions of the lead region, the Green's functions of therespective shell regions (g_(l1), g_(l2) . . . g_(ln)) can then becombined to arrive at the interface Green's function g_(l) at thelead/device interface (See, e.g., equation (2)). The device Green'sfunction is then solved with the interface Green's function according toequation (3) and the Keldysh equation. All observables are then deducedfrom the Green's functions as commonly done in Green's functionapproaches.

g _(li)=(E−H _(li) −H _(li,li-1) g _(li-1) H _(li,li-1))⁻¹  (2)

G ^(R)=(E−H _(d) −H _(d,l) g _(l) H _(l,d))⁻¹  (3)

Any suitable number of layers and/or thickness of layers may be used inthe lead region. In one embodiment, the thickness of the respectiveshells or partitions depends on the distance range of directmolecule-molecule interactions in the liquid/solvent. With this in mind,the thickness of each shell region layer is preferably kept at a minimumto minimize the computational load for each respective shell region.

FIG. 5 shows a block diagram of an exemplary embodiment of a liquidsystem simulation system 100 which can be used to generate, analyze,and/or utilize the model for open quantum liquid boundary conditionsdiscussed above in relation to FIGS. 1 and 2 . The liquid systemsimulation system 100 is typically provided in a housing, cabinet, orthe like 102 that is configured in a typical manner for a computingdevice. In one embodiment, the liquid system simulation system 100includes processing circuitry/logic 104, memory 106, a power module 108,a user interface 110, and a network communications module 112. It isappreciated that the illustrated embodiment of the liquid systemsimulation system 100 is only one exemplary embodiment of a liquidsystem simulation system 100 and is merely representative of any ofvarious manners or configurations of a simulation system, personalcomputer, server, or any other data processing systems that areoperative in the manner set forth herein.

The processing circuitry/logic 104 is configured to execute instructionsto operate the liquid system simulation system 100 to enable thefeatures, functionality, characteristics and/or the like as describedherein. To this end, the processing circuitry/logic 104 is operablyconnected to the memory 106, the power module 108, the user interface110, and the network communications module 112. The processingcircuitry/logic 104 generally comprises one or more processors which mayoperate in parallel or otherwise in concert with one another. It will berecognized by those of ordinary skill in the art that a “processor”includes any hardware system, hardware mechanism or hardware componentthat processes data, signals, or other information. Accordingly, theprocessing circuitry/logic 104 may include a system with a centralprocessing unit, multiple processing units, or dedicated circuitry forachieving specific functionality.

The memory 106 may be of any type of device capable of storinginformation accessible by the processing circuitry/logic 104, such as amemory card, ROM, RAM, write-capable memories, read-only memories, harddrives, discs, flash memory, or any of various other computer-readablemedium serving as data storage devices as will be recognized by those ofordinary skill in the art. The memory 106 is configured to storeinstructions including a liquid system simulation program 114 forexecution by the processing circuitry/logic 104, as well as data 116 foruse by the liquid system simulation program 114.

With continued reference to FIG. 5 , the power module 108 of the liquidsystem simulation system 100 is configured to supply appropriateelectricity to the liquid system simulation system 100 (i.e., includingthe various components of the liquid system simulation system 100). Thepower module 108 may operate on standard 120 volt AC electricity, butmay alternatively operate on other AC voltages or include DC powersupplied by a battery or batteries.

The network communication module 112 of the liquid system simulationsystem 100 provides an interface that allows for communication with anyof various devices using various means. In particular, the networkcommunications module 112 may include a local area network port thatallows for communication with any of various local computers housed inthe same or nearby facility. In some embodiments, the networkcommunications module 112 further includes a wide area network port thatallows for communications with remote computers over the Internet.Alternatively, the liquid system simulation system 100 communicates withthe Internet via a separate modem and/or router of the local areanetwork. In one embodiment, the network communications module isequipped with a Wi-Fi transceiver or other wireless communicationsdevice. Accordingly, it will be appreciated that communications with theliquid system simulation system 100 may occur via wired communicationsor via the wireless communications. Communications may be accomplishedusing any of various known communications protocols.

The liquid system simulation system 100 may be operated locally orremotely by a user. To facilitate local operation, the liquid systemsimulation system 100 may include an interactive user interface 110. Viathe user interface 110, a user may access the instructions, includingthe liquid system simulation program 114, and may collect data from andstore data to the memory 106. In at least one embodiment, the userinterface 110 may suitably include an LCD display screen or the like, amouse or other pointing device, a keyboard or other keypad, speakers,and a microphone, as will be recognized by those of ordinary skill inthe art. Alternatively, in some embodiments, a user may operate theliquid system simulation system 100 remotely from another computingdevice which is in communication therewith via the network communicationmodule 112 and has an analogous user interface.

As discussed above, the liquid system simulation system 100 includes aliquid system simulation program 114 stored in the memory 106. Theliquid system simulation program 114 is configured to enable to liquidsystem simulation system 100 to perform calculations of carriertransport properties, quantum properties and/or other observablecharacteristics (e.g., density, solubility, reactivity, stability,optical spectra, thermal spectra, magnetic properties, susceptibility,and the like) pertaining to one or more simulation models of the system.

As will be discussed in further detail below, the liquid systemsimulation program 114 improves upon conventional simulation methods byenabling multi-scale simulations that reflect an accurate andquantitative understanding of quantum mechanics-dominated carrier flowin an entire realistically extended complex device. To accomplish this,the liquid system simulation program 114 partitions a model of a system,such as a liquid system, or molecule in solvent system, into a sphericaldevice region and a plurality of spherical cell lead regions. Thesimulation program is configured to apply any suitable method oralgorithm to the partitioned model to derive selected properties for thesystem being modeled. Examples of such methods and algorithms includeNEGF, RGF, nonlocal RGF, DFT, Wannier Functions, etc.

In one exemplary embodiment, the data 116 includes material parameterfiles 118 and simulation input decks 120. The material parameter files118 and simulation input decks 120 include data which defines thestructure of the nanoelectronic device to be simulated, as well asvarious parameters of the simulation to be performed. The materialparameter files 118 and/or simulation input decks 120 describe thestructure of the liquid system device at an atomic level, and mayinclude information such as geometries, types of materials, dopinglevels, crystal structures, and other physical characteristics.Additionally, the material parameter files 118 and/or simulation inputdecks 120 may describe simulation parameters such as bias voltages,input currents, ambient conditions, physical constants, values forexperimentally determined parameters, simulation settings, etc. In someembodiments, the simulation input decks 120 are written in a suitableinput deck programming language.

The liquid system simulation program 114 receives the material parameterfiles 118 and simulation input decks 120 as inputs and utilizes one ormore models, algorithms, and/or processes to calculate carrier transportcharacteristics, or other physical phenomena, of the device defined bythe respective material parameter files 118 and simulation input decks120. In at least one embodiment, the liquid system simulation program114 is configured to provide the calculated carrier transportcharacteristics or other physical phenomena in the form of an outputfile which can be used by another program. In some embodiments, theliquid system simulation program 114 is configured to operate a displaydevice of the user interface 110 to display a graphical depiction of thecalculated carrier transport characteristics or other physicalphenomena, such as a graph, plot, diagram, or the like.

With continued reference to FIG. 5 , the liquid system simulationprogram 114 includes one or more simulation models for open quantumliquid boundary conditions configured to simulate carrier transportcharacteristics, quantum properties and/or other physical phenomena of aparticular liquid system. In the description of the methods andalgorithms described herein, statements that the method or model isperforming some task or function refers to a general purpose processor,controller, or the like executing programmed instructions stored innon-transitory computer readable storage media operatively connected tothe processor to manipulate data or to operate one or more components inthe liquid system simulation system 100 to perform the task or function.Particularly, the processing circuitry/logic 104 above may be such aprocessor and the executed program instructions may be stored in thememory 106. Additionally, the steps of the methods may be performed inany feasible chronological order, regardless of the order shown in thefigures or the order in which the steps are described.

While the disclosure has been illustrated and described in detail in thedrawings and foregoing description, the same should be considered asillustrative and not restrictive in character. It is understood thatonly the preferred embodiments have been presented and that all changes,modifications and further applications that come within the spirit ofthe disclosure are desired to be protected.

What is claimed is:
 1. A method of determining at least one property ofa liquid system using a modeling system, the liquid system including atleast one molecule in a solvent, the modeling system including aprocessor, the method comprising: generating a quantum model of theliquid system using the processor of the modeling system, the quantummodel including a device region and a lead region, the device regionbeing spherical in shape and encompassing the at least one molecule anda portion of the solvent of the liquid system, the lead regionencompassing a region of the solvent surrounding the device region,determining a first property of the device region by solving a firstquantum equation for the device region using the processor of thesystem; determining the first property of the lead region by solving thefirst quantum equation under open boundary conditions for the leadregion using the processor of the system; and combining the firstproperty of the device region with the first property of the lead regionto arrive at a total first property for the liquid system using theprocessor of the system.
 2. The method of claim 1, wherein the firstquantum equation comprises a non-equilibrium Green's function (NEGF). 3.The method of claim 1, further comprising: determining a Hamiltonian forthe liquid system; and solving the NEGF with reference to theHamiltonian.
 4. The method of claim 3, wherein the Hamiltonian isdetermined using a Wannierization procedure.
 5. The method of claim 1,further comprising: partitioning the lead region into a plurality ofnested spherical, paraboloid, cubic or otherwise shaped shell regionsstarting from a device/lead interface which defines where the deviceregion meets the lead region; and solving the first quantum equationrecursively for the plurality of spherical, paraboloid, cubic orotherwise shaped shell regions to determine the first property for thelead region.
 6. The method of claim 5, wherein the first quantumequation is a NEGF, and wherein the NEGF is solved using a recursiveGreen function (RGF) method.
 7. The method of claim 6, wherein dephasingincreases with distance from the device region which results in thespherical, paraboloid, cubic or otherwise shaped shell regions that arefarther away from the device region having less non-locality than thespherical, paraboloid, cubic or otherwise shaped shell regions that arecloser to the device region, and wherein a number of matrix inversionsrequired to solve the NEGF for a given region depends in part on theamount of non-locality in the region.
 8. The method of claim 1, furthercomprising: receiving model parameters for the liquid system as input tothe processor, the model parameters identifying at least one of a typeof molecule and a type of solvent to be modeled for the liquid system.9. A non-transitory computer readable medium storing a plurality ofinstructions which are configured to, when executed, cause at least oneprocessor to execute a method of determining at least one property of aliquid system, the liquid system including at least one molecule in asolvent, the method comprising: generating a quantum model of the liquidsystem using the processor of the modeling system, the quantum modelincluding a device region and a lead region, the device region beingspherical, paraboloid, cubic or arbitrary in shape and encompassing theat least one molecule and a portion of the solvent of the liquid system,the lead region encompassing a region of the solvent surrounding thedevice region, determining a first property of the device region bysolving a first quantum equation for the device region using theprocessor of the system; determining the first property of the leadregion by solving the first quantum equation under open boundaryconditions for the lead region using the processor of the system; andcombining the first property of the device region with the firstproperty of the lead region to arrive at a total first property for theliquid system using the processor of the system.
 10. The non-transitorycomputer readable medium of claim 9, wherein the first quantum equationcomprises a non-equilibrium Green's function (NEGF).
 11. Thenon-transitory computer readable medium of claim 9, wherein the methodfurther comprises: determining a Hamiltonian for the liquid system; andsolving the NEGF with reference to the Hamiltonian.
 12. Thenon-transitory computer readable medium of claim 11, wherein theHamiltonian is determined using a Wannierization procedure.
 13. Thenon-transitory computer readable medium of claim 9, wherein the methodfurther comprises: partitioning the lead region into a plurality ofnested spherical, paraboloid, cubic or otherwise shaped shell regionsstarting from a device/lead interface which defines where the deviceregion meets the lead region; and solving the first quantum equationrecursively for the plurality of spherical, paraboloid, cubic orotherwise shaped shell regions to determine the first property for thelead region.
 14. The non-transitory computer readable medium of claim13, wherein the first quantum equation is a NEGF, and wherein the NEGFis solved using a recursive Green function (RGF) method.
 15. The methodof claim 6, wherein dephasing increases with distance from the deviceregion which results in the spherical, paraboloid, cubic or otherwiseshaped shell regions that are farther away from the device region havingless non-locality than the spherical, paraboloid, cubic or otherwiseshaped shell regions that are closer to the device region, and wherein anumber of matrix inversions required to solve the NEGF for a givenregion depends in part on the amount of non-locality in the region. 16.The non-transitory computer readable medium of claim 9, wherein themethod further comprises: receiving model parameters for the liquidsystem as input to the processor, the model parameters identifying atleast one of a type of molecule and a type of solvent to be modeled forthe liquid system.